Variation measure ($|\mu |$)

For a finite signed or complex measure $\mu$, its variation is the positive measureIt controls integration by $|\int fd\mu |\le \int |f|d|\mu |$.

The total variation norm of a finite signed or complex measure is the total mass of its variation measure. Under the Riesz-Markov-Kakutani representation theorem, it equals the norm of the corresponding member of $C(K{)}^{\ast }$.